EXTINCTION THRESHOLD IN RANDOM HETEROGENEOUS CONDENSED MIXTURES WITH AN EXTREMELY SMALL AMOUNT OF A COMBUSTIBLEO. S. Rabinovich and P. S. Grinchuk UDC 536.46 A mathematical model describing the process of combustion of heterogeneous condensed mixtures with account for the randomness of the distribution of combustible particles over the system is proposed. The step dependence of the reaction rate on the temperature is used as a model of chemical kinetics. The case where the concentration of the particles is extremely low but the heat energy released in their combustion is high has been investigated. It is shown that for an adiabatic system there exists a concentration limit of combustion. The relation of this combustion limit to the geometric phase transition occurring in a heterogeneous condensed mixture with rare combustion inclusions has been demonstrated. An analytical approach to the evaluation of the threshold concentration of the combustible in such systems, based on the continual theory of percolation, is proposed. A. V. Luikov Heat and Mass Transfer Institute, National Academy of Sciences of Belarus, Minsk, Belarus; email: firstname.lastname@example.org, email@example.com. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 76, No. 2, pp. 80-87, March-April, 2003. Original article submitted November 13, 2002.